Using the following dimensional scales x' = x/l; y' = y/l; u' = u/U; v' = v/U; p' = p/(pU²); B' = B/(pU²/1); 0 = (T-Tr)/AT; Re = UL/v; Pr = v/a; Sc = v/Dab, show that the governing equations can be written in the following non-dimensional form: continuity: x-motion: y-motion: Energy: Species a: du' Əv' ax' ay' du' əx² u' = 0 ·+v' dy' Əv' u' '+v'. ax' dy' du' ში u'+v'. awд əx' de dy' = - 3 ƏWA dy' ·+v': ra²u' a²u' Relax + 1 a²0 Re Prax' ap' 1 -p+2 (²+²) + B dy¹² +242) + 1 (J²WA + a² WA) ay¹² ²) + B's Re Sc ax¹²
Using the following dimensional scales x' = x/l; y' = y/l; u' = u/U; v' = v/U; p' = p/(pU²); B' = B/(pU²/1); 0 = (T-Tr)/AT; Re = UL/v; Pr = v/a; Sc = v/Dab, show that the governing equations can be written in the following non-dimensional form: continuity: x-motion: y-motion: Energy: Species a: du' Əv' ax' ay' du' əx² u' = 0 ·+v' dy' Əv' u' '+v'. ax' dy' du' ში u'+v'. awд əx' de dy' = - 3 ƏWA dy' ·+v': ra²u' a²u' Relax + 1 a²0 Re Prax' ap' 1 -p+2 (²+²) + B dy¹² +242) + 1 (J²WA + a² WA) ay¹² ²) + B's Re Sc ax¹²
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
Transcribed Image Text:Using the following dimensional scales x' = x/l; y' = y/l; u' = u/U; v' = v/U; p' = p/(pU²);
B' = B/(pU²/1); 0 = (T-T.)/AT; Re = UL/v; Pr = v/a; Sc = v/Dab, show that the governing
equations can be written in the following non-dimensional form:
continuity:
x-motion:
y-motion:
Energy:
Species a:
du'
ax'
u
+3y= 0
u'
du'
ax'
Əx'
+v'
du'
Əy'
+v'. ==
ay'
30
u' +v'.
Əx'
ƏWA
ax'
де
dy!
+v'
aw A
Əy'
др'
ax'
(0²u'
a²u'
+ + 2/12 (3²1/²/² + 0²1/²1) + Bx
Reax¹²
dy'
=
ap' -1 (2²0² + 3²1/²) + By
+
ay' Reax¹²
dyr²
1 a²0 a²0
dyr²
Re Prax¹²
+
1
ResTWA +2
J²WA
ax¹2
ay ¹2
Expert Solution
Step 1: Convert variables into reference variables
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